realizing tunable inverse and normal doppler shifts in reconfigurable rf metamaterials

www.nature.com/scientificreports OPEN Realizing Tunable Inverse and Normal Doppler Shifts in Reconfigurable RF Metamaterials received: 14 January 2015 accepted: 29 May 2015 Published: 26 June 2015 Jia Ran1, Yewen Zhang1, Xiaodong Chen2,3, Kai Fang1, Junfei Zhao1, Yong Sun1 & Hong Chen1 The Doppler effect has well-established applications in astronomy, medicine, radar and metrology Recently, a number of experimental demonstrations of the inverse Doppler effect have begun to appear However, the inverse Doppler effect has never been observed on an electronically reconfigurable system with an external electromagnetic wave source at radio frequencies (RF) in experiment Here we demonstrate an experimental observation of the inverse Doppler shift on an electronically reconfigurable RF metamaterial structure, which can exhibit anomalous dispersion, normal dispersion or a stop band, depending on an applied bias voltage Either inverse or normal Doppler shift is realized by injecting an external RF signal into the electronically reconfigurable metamaterial, on which an electronically controllable moving reflective boundary is formed The effective velocity of this boundary and the resulting frequency shift can be tuned over a wide range by a digital switching circuit This work is expected to open up possibilities in applying the inverse Doppler effect in wireless communications, radar and satellite navigation The Doppler effect is caused by the fact that the relative motion between a source and a detector will lead to a frequency shift in the received signal In media of normal dispersion (right-handed), an approaching source increases the received signal frequency, whereas a receding source decreases it However, in media of anomalous dispersion (left-handed) it has been proved in theory that an inverse Doppler effect occurs, that is, an approaching source decreases the received signal frequency, whereas a receding source increases it1 This counter-intuitive inverse Doppler effect was theoretically investigated by Veselago in 1968 in a material with simultaneously negative permittivity and negative permeability, since the group velocity and phase velocity are in the opposite directions in these double negative materials (DNG)1 Such a material, now known as a metamaterial, was realized physically by Pendry, Smith et al around 20002–4 and has since been extensively studied by others5–10 Until now there have been only a few inferred measurements of the inverse Doppler effect in metamaterials at radio frequencies Based on the approach proposed by Kozyrev et al.11,12, the first experimental demonstration of the inverse Doppler effect at radio frequency was reported by Seddon and Bearpark13 In their experiment, the RF waves were not injected directly from an external source, but were excited by a moving shock wave on the magnetic nonlinear transmission line (an internal source) and bounced between the front of the pump pulse and the input terminal of the line Hence, their work, referred to as the indirect experimental measurement in Ref 14, not only causes a controversy in the interpretation of the results15,16, but also is not complete, since the frequency down-shifted signal does not exist17 Leong et al.18 and Yuan et al.19 have also demonstrated the inverse Doppler effect along a left-handed transmission line using an internal source in the circuit simulation Their internal effective moving source was modeled by using sequential fast switches on the transmission line Also, Kozyrev et al.20 observed the inverse Doppler shift with an external RF signal on a magnetic nonlinear transmission line in simulation Tongji University, Shanghai, 200092, China 2University of Electronic Science and Technology of China, Chengdu, 610054, China 3Queen Mary University of London, E1 4NS, UK Correspondence and requests for materials should be addressed to Y.Z (email: yewen.zhang@tongji.edu.cn) or X.C (email: xiaodong.chen@qmul.ac.uk) Scientific Reports | 5:11659 | DOI: 10.1038/srep11659 www.nature.com/scientificreports/ Figure 1.  Illustration of the experimental set-up used to demonstrate inverse and normal Doppler shifts a, The whole set-up used to test Doppler shifts V(xi,t)(i =  1,2…14) are the bias voltages provided to the CRLH TL units Two different colors on the reflective boundary controller stand for two different voltages, which leads to the different characteristics of the corresponding units of the transmission line The units of the transmission line in gray lie in passband (either right-handed or left-handed), while the CRLH TL units in brown are set in band gap The reflective boundary at the interface between the two kinds of units can move at the velocity of vs by switching the bias voltages supplied by the external controlling circuit b, Schematic of the unit of the CRLH TL The reflective boundary controller provides the bias voltage V(xi,t) to the varactors through a ferrite bead which prevents the incident wave propagating from the CRLH TL to the controller lately In addition, the inverse Doppler effect was observed experimentally at optical and acoustic frequencies14,21, and was also observed when magnons (magnetostatic spin wave ) reflected from a moving solid object and magnonic crystal in the gigahertz frequency range22,23 This has motivated us to explore an experimental observation of the inverse Doppler effect with an external RF source on an electronically reconfigurable composite right-left handed transmission line (CRLH TL), which was originally proposed by Eleftheriades and Carloz et al as a convenient 1-D metamaterial structure24–27 By loading such a transmission line with the varactors28, we have further extended its reconfigurability, by arranging that the dispersion characteristics of each line section can be controlled electronically through a digital switching circuit (later referred to as a reflective boundary controller) By controlling the bias voltage, each section of the transmission line can exhibit normal dispersion (right-handed), anomalous dispersion (left-handed/DNG), or a stop band (band gap) An electronically controllable moving reflective boundary can be formed between the regions of either normal transmission, anomalous dispersion and a band gap, by means of the reflective boundary controller When an external RF signal is injected into this tunable transmission line, shown schematically in Fig.  1a, the reflected wave from the moving reflective boundary can be treated as an effective source approaching or receding from the detector While the passband section of the transmission line is set to be in normal dispersion mode (right-handed) by choice of its bias voltage, the group and phase velocities of the wave are in the same direction Hence, the normal Doppler effect occurs in this situation If the passband section is set to be in anomalous dispersion mode (left-handed), the group and phase velocities of the wave are in opposite directions Consequently, when the reflective boundary is approaching or receding from the detector, the phase velocity of the wave is actually receding from or approaching the detector, Scientific Reports | 5:11659 | DOI: 10.1038/srep11659 www.nature.com/scientificreports/ leading to the inverse Doppler effect Hence, either the inverse Doppler effect or the normal Doppler effect (both frequency up-shifted and down-shifted) can be realized by applying a suitable switching mode of the controlling voltage on this CRLH transmission line Results Theoretical Doppler frequency shifts.  The frequency of the reflected wave fr and the frequency of the incident wave fi have following relationship13: fr fi = − (→ vs⋅→ v i)/ vi2 − (→ v ⋅→ v )/ v s r r ( 1) where vs, vi, vr are the velocities of the moving reflective boundary, incident wave phase velocity and reflected wave phase velocity, respectively Therefore the Doppler shift can be calculated as: ∆f = f r − f i (2) Equations (1) and (2) have been used to predict the inverse and normal Doppler shifts The difference between the inverse and normal Doppler effects is that the directions of the electromagnetic waves are opposite, since the phase velocity is antiparallel with the group velocity in double negative materials and parallel in normal materials The dispersion of the CRLH TL is linear and the velocity of the incident wave varies slightly in the Doppler shift range, as shown in Supplementary Fig 6, hence we have approximately → v i ≈ −→ v r The theoretical velocity of the incident wave in the transmission line can be obtained easily from the theoretical dispersion function (see Supplementary Information S-II for details) The Doppler frequency shifts have also been obtained by using Keysight (Agilent) ADS (Advanced Design System) simulator Characteristics of the tunable composite right-left handed transmission line.  The unit of the composite right-left handed transmission line comprised sections of microstrip line, each loaded with two NXP BB135 varactor diodes in series and one in parallel, as shown in Fig.  1b In addition, two inductors LS in series and one LP in parallel are chosen to select the operating frequency When the bias voltages changes, the capacitances of the three varactors change - leading to variation of the dispersion curve The characteristics of the CRLH TL unit are simulated using Keysight (Agilent) ADS simulator, a commonly used RF circuit modeling tool Figure 2a shows the theoretical dispersion curves of the CRLH TL as a function of the bias voltages which are calculated by considering the transmission line as a cascade network (see Supplementary Information S-II) The gray plane at 1 GHz cuts across the upper branches (right-handed passband), the band gap, and the lower branches (left-handed passband) of the dispersion curves under different bias voltages The red, green and dark curves correspond to the dispersion under bias voltages of 6 V, 11 V and 24 V, respectively Figure 2b shows the simulated transmission, in terms of |S21|, under different bias voltages Because of inaccuracy of the varactor circuit model in ADS, the bias voltages in simulation needed to be set slight differently from those in the theoretical model, i.e 5 V, 11 V and 23 V for achieving the equivalent transmission characteristics (as shown in Supplementary Fig 7b) Both figures indicate that with the increased bias voltages, the propagation characteristics at 1 GHz change from right-handed transmission to a band gap (stop-band transmission), and then to left-handed transmission The measured transmission |S21| at 1 GHz at three voltages of 6 V, 11 V and 24 V is illustrated in Fig. 2c In the experiments, a 14-unit CRLH transmission line was built and connected to a reflective boundary controller that separately provides the bias voltages to each transmission line unit, as shown in Fig. 1a If the left-hand sections of the transmission units are set in the passband mode and the right-hand sections are set in the band gap mode by providing different bias voltage to the transmission line units, a reflective boundary will appear at the interface between the passband and the band gap sections The reflective boundary can move either towards or away from the detector by regulating the bias voltages to each CRLH TL unit and by choosing the proper wave incident direction For convenience of testing, the wave is emitted into the CRLH TL from either the left end or the right end For instance, as Fig.  1a shows, bias voltages of the left CRLH TL units (gray) are at either 6 V or 24 V, setting these units in the transmission mode (right-handed or left-handed), while the bias voltages of right CRLH TL units (brown) are at 11 V, setting these units in band gap mode By this means a reflective boundary is formed at the interface of these two groups of CRLH TL units Changing the bias voltages of the TL unit to the right of the reflective boundary would switch the unit from band gap to passband, so the reflective boundary will move one unit to the right By stepping the change in bias voltages sequentially rightwards, we obtain a rightwards moving reflective boundary, moving away from the detector at the left hand end of the structure The effective velocity of the boundary vs can be controlled by regulating the time interval of the pulse signal in the reflective boundary controller and is positive when the boundary moves away from the source The reflective boundary could be considered moving smoothly when the wavelength is considerably larger than the length of the transmission unit For an incident wave in the leftwards direction, we can achieve a reflective boundary moving towards the detector if the left part of Scientific Reports | 5:11659 | DOI: 10.1038/srep11659 www.nature.com/scientificreports/ Figure 2.  The voltage-dependent transmission characteristics a, Theoretical dispersion curves under different bias voltages The gray plane indicates the working frequency 1 GHz, while the red, green and dark curves correspond to three typical bias voltages (6 V, 11 V and 24 V) b, Simulated |S21| under different bias voltages The branch above is the right-handed passband while the branch blow is the left-handed passband The dark diamond markers are a set of bias voltages (5 V, 11 V and 23 V) at 1 GHz for achieving the equivalent transmission characteristics in a c, Measured |S21| verse frequency at the three bias voltages shown in a the TL is set in band gap mode while the right part is set in passband mode By these means both inverse and normal Doppler shifts can be realized in the experiments under proper control of the bias voltages and the location of the incident wave Measured Doppler frequency shifts.  In the experiments, the wavelength of the incident wave at 1 GHz is 88.6 mm in the left-handed passband and 151.1 mm in the right-handed passband; both are much longer than each unit of the CRLH TL (d0 =  14.2 mm) The effective velocity of the reflective boundary is in the range 17.8–71.0 km/s The corresponding inverse Doppler shift is between –0.385 MHz and –1.465 MHz (for vs   0) and the normal Doppler shift is between + 1.125 MHz and + 0.26 MHz (for vs   0) The direction of the incident wave should be different according to the different sets of edges and bias voltages, as discussed below Figure  shows a comparison between the theoretical, simulated and experimental results of the Doppler frequency shifts in the different scenarios indicated as I to IV In condition I (the left section of TL is set in high bias voltage Vh =  24 V(left-handed passband) while the right section of TL is set in low bias voltage Vi =  11 V(stop band); the wave is injected from the left end), the reflective boundary is moving away from the detector in the left-handed passband (vs >  0) In condition II (the left section of TL is set in Vh =  11 V(stop band) while the right section of TL is set in Vi =  6 V(right-handed passband); the wave is injected from the right), the reflective boundary is approaching the detector in the right-handed passband (vs